Nope. A rooster makes no difference at all in the frequency of egg laying. The hens will lay their eggs on their schedule regardless of whether a rooster, or other hens, or anything is there. The only difference he makes is if he's mating the hens then the eggs will be fertile, and if he's not mating the hens the eggs will not be fertile.

Living the good life in Oregon with my husband, dog, two-and-a-half cats, 18-ish rabbits, and 4-ish chickens.